Modeling the effect of permeability anisotropy on the steam-assisted gravity drainage (SAGD) process in multi-layered reservoirs

The performance of the SAGD process is significantly impacted by permeability anisotropy both during the initial rise of the steam chamber as well as during the lateral spreading of the steam chamber. Previous models for SAGD performance take into account the effective permeability of the medium but don't explicitly account for the anisotropy. We extend our earlier development of a semi-analytical model that accounts for permeability anisotropy during the SAGD process to multi-layered reservoirs. We explicitly account for permeability anisotropy by resolving the resultant oil drainage and resultant gravity head vectors on to the principal axes of the reservoir's permeability ellipsoid. The extension to multi-layered systems recognizes that the entire reservoir may not be characterized by a single anisotropy ratio and in fact the ratio may vary from one reservoir layer to the next. We model oil recovery in such situations taking into account the unique quasi-steady state flow characteristics of the SAGD process. Our method involves using the quasi-steady assumption to derive the appropriate SAGD slope drainage equations for both the resultant gravity head (RGH) and the resultant oil discharge (ROD) vector orientations. These vectors are later mapped to the principal anisotropy axes of the permeability field. The entire modeling is done in dimensionless space making the model suitable for use as predictive type-curves. Our results show that just like for the single layer case, both the RGH and ROD models give different results especially at low equivalent anisotropy ratios. We also show that there is a limitanisotropy ratio beyond which the anisotropy ceases to affect the production characteristics. Moreover, our results show that static averaging techniques like arithmetic, harmonic averaging that yield effective permeability used in traditional models for the SAGD process fail to capture the effect of anisotropy on SAGD flow rates for multi-layered reservoirs. The resulting production expression can be used as a fast proxy to model the SAGD process in more complex reservoirs for the purposes of history matching and/or in a predictive modeling framework.